1. Field of the Invention
The present invention relates generally to the field of rotating shafts, and more particularly to a method of and apparatus for determining the origins and magnitudes of dynamic torsion loads nonintrusively from measurements of specifically combined discrete counterparts of twist and angular velocity, and determination of related parameters from various known and applied conditions related thereto.
2. Description of the Background Art
Under steady state (time-independent) conditions, there is a net balance between the torque components applied to a shaft. For example, a time-independent torque applied to a shaft of a marine propulsion system by an engine is exactly balanced under steady state conditions by a time-independent torque of equal magnitude and opposite sign from the drag of a ship's propeller. In practice, time-independent torques are seldom truly realized for power systems with natural periods, such as those due to cylinders or propellers. Experimental results have shown that angular velocity of such a propulsion system fluctuates about some average. The frequency spectrum of the angular velocity contains peaks due to the periodicity of the torque developed by the engine driving system or the torque of the output load, e.g., a propeller in air or water, as well as due to the natural frequencies of the shaft.
The relation between a time-independent torque T(x) applied at a point x along the axis of a shaft and the shear strain .phi.(x) produced on the surface of the shaft at that point is given by equation (1). EQU T(x)=(.pi./2)(G).phi.(x)(R.sup.4 -r.sup.4)/R (1)
where G is the shear (Lame) modulus, and R and r are the outer and inner radii of the circular shaft, respectively. The shear strain is related to the angular displacement .theta.(x,t) on the surface of the shaft by equation (2). EQU .phi.(x,t)=-R.differential..theta.(x,t)/.differential.x (2)
The quantity equation (3) is the differential twist. EQU .theta..sub.x (x,t)=.differential..theta./.differential.x (3)
Conventionally, steady state torques have been determined by measuring shear strain, for example, by a strain gauge. Under steady state conditions, a measurement of .phi. or, equivalently, of .theta..sub.x is by itself sufficient to determine the torque through relations (1) and (2). This method of determining steady state torque by measuring the twist or the shear strain and relating it to the torque by equation (1) is well known to those of ordinary skill in the art. Steady state torque is the only torque that can be determined by existing torque meters.
Existing torque meters are based on the measurement of twist and relating torque to that measurement through equations (1) and (2). The torque is thus assumed to be directly proportional to twist or shear strain. This assumption of proportionality, though valid for steady state torques, is incorrect when the load torque and engine torque are varying and unequal (time varying torques, or dynamic conditions). Although equation (2) for shear strain in terms of twist remains valid under dynamic conditions, the relation between torque and twist given by equation (1) does not. For unequal load and engine torques, the single measurement of twist represents a combination of the multiple torques; it cannot in principle determine either one of them individually, differentiate one from another nor determine which one is changing. Existing torque meters are inherently inaccurate to the extent that equilibrium is violated because their operation is based on the equation that is invalid for time dependent torques. The fact that equation (1) is derived from statics (T(x) is independent of both time and the shaft mass) limits the validity of any instrumentation system based on this equation to equilibrium (time independent) conditions.
In practice, existing torque meters are often used under dynamic conditions; such use is in error because the assumption of equilibrium underlying such meters is invalid. The result is that they are sensitive to a weighted average of the applied dynamic torques that cause accelerations. For sufficiently slow changes in torque, the error associated with applying existing torque meters to dynamic torques may be small and the measurement adequate for some applications. However, the size of the error cannot be determined by such time independent techniques. Furthermore, this error cannot be eliminated by calibration of the engine system under a given set of operating conditions because the weighting factors themselves depend on dynamic conditions and cannot be determined during normal operation by existing systems. Thus, measurement accuracy under dynamic conditions cannot be determined. Prior art torque meters are further incapable of determining the time required for a response (e.g., to a changing applied torque) to propagate along the system. The velocity of propagation of the response, called the torsional wave velocity, may be utilized in a number of ways and is not presently employed in the prior art.
Additionally, existing torque meters use values of the shear modulus calibrated prior to the assembly of the power system, normally at room temperature. Under actual operation conditions, the bulk parameters of the system (such as, for example, shaft moment of inertia, density of shaft material, shear modulus, speed of torsional waves, etc.) often change and/or are functions of position along the shaft. For example, changing and/or elevated temperatures are characteristic of advanced propulsion systems; the change in the value of the shear modulus over the operating temperature range of such systems is known to lead to an error of as much as 5-10% in the determination of torque, even at steady state, if this change is not taken into account. The temperature dependence of the shear modulus cannot generally be taken into account in existing torque meters. Variations in the shear modulus caused by varying temperatures, by position gradients, and by aging effects, such as fatigue, are not accounted for by existing systems. These systems cannot provide absolute calibration in the field. Significant sources of error are thereby introduced even for steady state conditions, where the method of existing torque meters is valid in principle.
Finally, torsional vibrations have, to date, been identified as sources of error which complicate computations of shaft characteristics. For some applications, the effect of torsional vibrations is to render measurement and calculation of shaft characteristics meaningless. Therefore, existing systems attempt to minimize the vibrations for the purposes of measurement and calculation. This represents an incomplete attempt to account for real-life effects, and measurements and calculations based on such methods are inherently inaccurate.
Hence, for significantly dynamic torques, for applications requiring high precision, for all applications requiring knowledge of the origin and magnitude of changing torques, existing torque meters cannot, in practice or even in principle, provide adequate data. The precision of existing torque meters is in fact limited by the operating principles on which they are based.